coming from the embeddings \(\bar{K} \hookrightarrow \bar{K}_p\) . We gather the necessary information on this map from the Poitou-Tate nine-term exact sequence [1]}, which in the case that \(S\)  is the set of all places is given by
\(\begin{tikzcd}0 & H^0(K,T) & H^0(_K,T) & H^2(K,T^*)^{\vee } &{}\\& H^1(K,T) {i_T} & H^1(_K,T) {(i_{T^*})^\vee } & H^1(K,T^*)^\vee &{}\\& H^2(K,T) & H^2(_K,T) & H^0(K,T^*)^\vee & 0,\end{tikzcd}\) 
